I previously posted standing wave current graphics from EZNEC. Here is another set covering multiple wavelengths. Please note that, unlike the standing wave current phasor, the magnitude of the traveling wave current phasor is constant and never zero. For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists. Just more evidence that a standing wave is not an EM wave.

Here's some previous information on the difference between a standing wave and a traveling wave.

I previously posted standing wave current graphics from EZNEC. Here is another set covering multiple wavelengths. Please note that, unlike the standing wave current phasor, the magnitude of the traveling wave current phasor is constant and never zero. For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists. Just more evidence that a standing wave is not an EM wave.

Just more evidence that you don't know what you're talking about. I guess you won't be satisfied until that's clear to everyone.

EZNEC is like a power tool. Anyone can pick it up but it's dangerous in the wrong hands.

Let me make an edit and add something, before we have to go through another round of this nonsense.

I'm going to explain to you what your phasor means. The radius of the helix (it's a helix since this is a traveling wave) is the amplitude of the wave (E0) and the angle around the axis is its phase (phi(z,t)). I'm using z for the position variable since that's what the document uses.

The electric field, for example, is E(z,t) = E0 sin(phi(z,t)). The amplitude (helix radius) doesn't change but the phase phi, and so the field, is a function of position and time. As the text above fig. 6 says, the whole figure slides along the z axis as time progresses. Your phasor helix is a snapshot in time, so its phase only depends on position. If we could see the time dependence it would turn like a screw.

Now the good part. The fact that the phasor helix doesn't go to zero does not mean that the electric field is always non-zero. Whenever phi passes through a multiple of pi (since I used sin in this example) the E field will be zero.

It sure looks like the electric and magnetic fields, which are in-phase in your traveling wave, do periodically go to zero as they reverse direction.

I've lost count of the straw men that you have attempted to set up for torture.

I was not talking about instantaneous values of E and H. I was talking about the ExH Poynting vector for plane waves which has a constant term indicating that the wave carries an average power. So let me upgrade my sentence:

"For real world EM waves, the average ExH value cannot fall to zero while the wave exists."

Question: What is the value of the Poynting vector for a pure standing wave?

There is no constant term. For a traveling wave in free space, the energy density E and energy flux S do go to zero whenever E and B are zero. The energy travels in bunches.

You're wrong, again.

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So let me upgrade my sentence:

"For real world EM waves, the average ExH value cannot fall to zero while the wave exists."

That's a statement entirely of your own making, based on your distinction between "real-world EM waves" (whatever that means) and something else.

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Question: What is the value of the Poynting vector for a pure standing wave?

This one I did work out for you (post #30). The energy density is

U = 0.5 eps0 E02 [ sin2(kx) sin2(wt) + cos2(kx) cos2(wt) ]

and the Poynting vector is

S = E x H = x (k E02/ w mu0) sin(kx) cos(kx) sin(wt) cos(wt)

= x (E02 / 4 Z0) sin(2kx) sin(2wt).

The behavior of the lowest mode, where the cavity walls are 1/2 wavelength apart, is the easiest to picture. During one cycle of the field (0 < wt < 2 pi), the energy density (given by the function U) starts at the walls (none in the middle), then flows to the middle (none at the walls), then back to the walls, two times. The energy oscillates twice as fast (frequency 2w) as the fields themselves.

The Poynting vector S describes the flow of the energy. It vanishes at the times of maximum energy density (all at the walls or all in the middle) since there is momentarily no flow at these peak times (like waves coming onto a beach, stopping, and then retreating). The energy flux reaches its peak values at the times between the energy peaks, as the energy moves back and forth. S is a vector quantity so its sign indicates its direction, positive means right, negative means left. S is positive between the left wall and the center as the energy there flows to the right, from the wall to the center, and, at the same time, negative between the right wall and the center as the energy there flows to the left, from that wall to the center. A quarter of a cycle later the sign of S reverses, as the energy flows back out to the walls.

As I also said before, the average value of S is zero and there is no net energy flow. That does not mean S is always zero.

Section 8.4.3 of the same document, also starting on page 15, describes the energy in standing waves, and gives essentially the same expressions that I derived. You can see that he switches freely between the two representations of a standing wave, namely as a single expression or as two opposing traveling waves (also in 8.3.3 where he deals with E and B). As I have always said, there is no physical or mathematical difference between the two viewpoints. Note the last paragraph of that section, at the top of page 16, where he says the energy flow in a standing wave is only zero on average, not identically zero.

Strange that this fellow also fails to mention "real-world EM waves." He just merrily switches back and forth between the two representations. Poor devil, he just doesn't realize the error of his ways.

BTW, you never thanked me for setting you straight about your phasors in my last post, when I was responding to your statement

"Please note that, unlike the standing wave current phasor, the magnitude of the traveling wave current phasor is constant and never zero. For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists."

I clearly showed that the fields (and energy) do go to zero, and your assumption that a constant-magnitude phasor somehow prevented this was completely wrong. You're welcome. I'm sure the fact that you failed to mention this was just an oversight.

This is absolutely my last post on this thread. You can follow this with any crazy ideas about "real-world EM waves" or anything else that you like. I will never respond to another of your posts. To the other readers of this forum I will only say buyer beware.

Bull. You never said anything about averages. You keep trying to get yourself out of this mess of your own creation.

OTOH, using that same logic, I never said anything about instantaneous values either so why did you "mistakenly" presume I was talking about instantaneous energy? If I refer to scalar values, like "energy" and "power", 99+% of the time I am talking about average energy and power. I don't find instantaneous energy and instantaneous power to be very useful concepts.

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You said, "For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists."

That's exactly what I said where "the electric and/or magnetic energy" was intended to imply the same meaning as the "average ExH energy". I used those colloquial words because a lot of readers here don't know what ExH means.

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There is no constant term. You're wrong, again.

Then your argument is with Ramo and Whinnery, not me. Reference: Fields and Waves in Communications Electronics; 3rd edition; Ramo, Whinnery, Van Duzer; page 143, Example 3.12c, "Poynting Flow in a Plane Wave". I'm going to use K for a constant involving permeability, permittivity, and the maximum envelope value.

Pz = K[1/2 + 1/2 cos 2(wt-kz)] (equation 18)

"Note that there is a constant term showing that the wave carries an average power, as expected. There is also a time-varying portion representing the redistribution of stored energy in space as maxima and minima of fields pass through a given region." (my emphasis)

Are you going to contact the publisher and demand that they correct the gross error that has been in that book for more than half a century?

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BTW, you never thanked me for setting you straight about your phasors in my last post, when I was responding to your statement

You want me to thank you for setting up a straw man and then knocking it down??? Virtually nothing of what I was trying to say disagrees with what you have said. Are you prone to tilting at windmills?

That EZNEC current envelope plot that I posted is a graphical indication that a standing wave is transporting zero average power while the traveling wave is indeed transporting some average power. (I'm using the IEEE definition of "power".) We'll just have to agree to disagree on that subject.

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